IJAIS publications are indexed with Google Scholar, NASA ADS, Informatics et. al.

## Call for Paper

-

#### January Edition 2023

International Journal of Applied Information Systems solicits high quality original research papers for the January 2023 Edition of the journal. The last date of research paper submission is December 15, 2022.

# Basic Edge Dominating Functions of Quadratic Residue Cayley Graphs

S. Jeelani Begum, B. Maheswari Published in Applied Mathematics

International Journal of Applied Information Systems
Year of Publication: 2013
10.5120/ijais12-450834
1. S.jeelani Begum and B.maheswari. Article: Basic Edge Dominating Functions of Quadratic Residue Cayley Graphs. International Journal of Applied Information Systems 5(1):24-27, January 2013. BibTeX

```@article{key:article,
author = "S.jeelani Begum and B.maheswari",
title = "Article: Basic Edge Dominating Functions of Quadratic Residue Cayley Graphs",
journal = "International Journal of Applied Information Systems",
year = 2013,
volume = 5,
number = 1,
pages = "24-27",
month = "January",
}
```

### Abstract

Graph Theory has been realized as one of the most useful branches of Mathematics of recent origin, finding widest applications in all most all branches of sciences, social sciences, and engineering and computer science. Nathanson[8] was the pioneer in introducing the concepts of NumberTheory, particularly, the "Theory of congruences" in Graph Theory, thus paving way for the emergence of a new class of graphs, namely, "Arithmetic Graphs". Cayley graphs are another class of graphs associated with the elements of a group. If this group is associated with some arithmetic function then the Cayley graph becomes an arithmetic graph. Quadratic residue is an arithmetic function which is defined by: Let p be an odd prime and n, a positive integer such that n 0 (mod p). If the quadratic congruence, has a solution then, n is called a quadratic residue mod p. The Quadratic Residue Cayley graph G(Zp , Q), is the Cayley graph associated with the quadratic residue function. The theory of basic edge dominating functions in Quadratic Residue Cayley Graphs is useful in the selection of modes, those are require to focus on the development of some connected systems like market management, operating system, banking , infrastructure system etc.

### Reference

1. Arumugam, S. , and Sithara Jerry. - Fractional edge domination in graphs, Appl. Anal. Discrete Math. 3 (2009), 359–370.
2. Arumugam, S. , and Velammal, S. - Edge domination in graphs, Taiwanese Journal of Mathematics, 2 (2) (1998), 173–179.
3. Cockayne, E. J. , and Mynhardt, C. M. - Convexity of extremal domination-related functions of graphs. In Domination in Graphs - Advanced Topics, (Ed. T. W. Haynes, S. T. Hedetniemi, P. J. Slater), Marcel Dekker, Inc. , New York, (1998), 109–131.
4. Haynes, T. W. , Hedetniemi, S. T. , and Slater, P. J. -Fundamentals of domination in graphs, Marcel Dekker, Inc. , New York (1998).
5. Haynes, T. W. , Hedetniemi, S. T. , and Slater, P. J. - Domination in Graphs: Advanced Topics, Marcel Dekker, Inc. , New York (1998).
6. Jeelani Begum, S. , Maheswari, B. , Edge Dominating Functions of Quadratic Residue Cayley Graphs International Journal of Computer Applications Vol 54(17), (2012), 47-49.
7. Mitchell, S. , and Hedetniemi, S. T. - Edge domination in trees. Congr. Numer. , 19 (1977), 489–509.
8. Nathanson, Melvyn B. - Connected components of arithmetic graphs, Monat. fur. Math, 29 (1980), 219 – 220.

### Keywords

Quadratic Residue Cayley Graph, Edge Domination, Edge Dominating Functions, Basic Edge Dominating Functions